Fundamental Dosimetry Quantities and Concepts: Review

Introduction to Medical Physics III: Therapy

Steve Kirsner, MS Department of Radiation Physics

Some Definitions

          SSD SAD Isocenter Transverse (Cross-Plane) Radial (In-plane) Sagittal Coronal Axial Supine Prone          Cranial Caudal Medial Lateral AP/PA Rt. & Lt. Lateral Superior Inferior RAO/RPO/LAO/LPO

Fundamentals

  Review of Concepts  Distance, depth, scatter effects Review of Quantities     PDD, TMR, TAR, PSF (definition/dependencies) Scatter factors Transmission factors Off-axis factors

Distance, Depth, Scatter

   Distance  From source to point of calculation Depth  Within attenuating media Scatter  From phantom and treatment-unit head

Distance, Depth, Scatter

Scatter Concepts

 Contribution of scatter to dose at a point   Amount of scatter is proportional to size and shape of field (radius). increase with increase in length Think of total scatter as weighted average of contributions from field radii. SAR, SMR

Equivalent Square

 The “equivalent square” of a given field is the size of the square field that produces the same amount of scatter as the given field, same dosimetric properties.

  Normally represented by the “side” of the equivalent square Note that each point within the field may have a different equivalent square

Effective Field Size

    The “effective” field size is that size field that best represents the irregular field’s scatter conditions It is often assumed to be the “best rectangular fit” to an irregularly-shaped field These are only estimates In small fields or in highly irregular fields it is best to perform a scatter integration

Effective Field Size

 Must Account for flash, such as in whole brain fields. Breast fields and larynx fields.

Blocking and MLCs

  It is generally assumed that tertiary blocking (blocking accomplished by field-shaping devices beyond the primary collimator jaws) affects only phantom scatter and not collimator or head scatter  Examples of tertiary blocking are (Lipowitz metal alloy) external blocks, and tertiary MLCs such as that of the Varian accelerator  When external (Lipowitz metal) blocks are supporte by trays, attenuation of the beam by the tray must be taken into account It is also generally assumed that blocking accomplished by an MLC that replaces a jaw, such as the Elekta and Siemens MLCs, modifies both phantom and collimator (head) scatter.

Effective Fields Asymmetric Field Sizes

  Must Account for locaton of Central axis or calculation point.

There is an effective field even if there are no blocks.

cax

…

Calc.

Pt.

Inverse Square Law

  The intensity of the radiation is inversely proportional to the square of the distance.

X 1 D 1 2 = X 2 D 2 2

Percent Depth Dose (PDD)

  PDD Notes Characterize variation of dose with depth.



Field size is defined at

the surface of the phantom or patient  The differences in dose at the two depths, d 0 and d, are due to:    Differences in depth Differences in distance Differences in field size at each depth

PDD



D d

/

D d

0

PDD: Distance, Depth, Scatter

 Note in mathematical description of PDD  Inverse-square (distance) factor   Dependence on SSD Attenuation (depth) factor  Scatter (field-size) factor

PDD: Depth and Energy Dependence

 PDD Curves   Note change in depth of d max Can characterize PDD by PDD at 10-cm depth  %dd 10 of TG-51

PDD: Energy Dependence

 Beam Quality effects PDD primarily through the average attenuation coefficient. Attenuation coefficient decreases with increasing energy therefore beam is more penetrating.

PDD Build-up Region

 Kerma to dose relationship    Kerma and dose represent two different quantities   Kerma is energy released Dose is energy absorbed Areas under both curves are equal Build-up region produced by forward scattered electrons that stop at deeper depths

PDD: Field Size and Shape

    Small field sizes dose due to primary Increase field size increase scatter contribution.

Scattering probability decreases with energy increase. High energies more forward peaked scatter.

Therefore field size dependence less pronounced at higher energies.

PDD: Effect of Distance

 Effect of inverse-square term on PDD  As distance increases, relative change in dose rate decreases (less steep slope)  This results in an increase in PDD (since there is less of a dose decrease due to distance), although the actual dose rate decreases

Mayneord F Factor

 The inverse-square term within the PDD   PDD is a function of distance (SSD + depth) PDDs at given depths and distances (SSD) can be corrected to produce approximate PDDs at the same depth but at other distances by applying the Mayneord F factor  “Divide out” the previous inverse-square term (for SSD 1 ), “multiply in” the new inverse-square term (for SSD 2 )

Mayneord F Factor

   Works well small fields-minimal scatter Begins to fail for large fields deep depths due to increase scatter component.

In general overestimates the increase in PDD with increasing SSD.

PDD Summary

      Energy- Increases with Energy Field Size- Increases with field size Depth- Decreases with Depth SSD- Increases with SSD Measured in water along central axis Effective field size used for looking up value

The TAR

 The TAR …   The ratio of doses at two points:    Equidistant from the source That have equal field sizes at the points of calculation

Field size is defined at point of calculation

Relates dose at depth to dose “in air” (free space)  Concept of “equilibrium mass”  Need for electronic equilibrium – constant Kerma-to-dose relationship

TAR



D d

/

D fs

The PSF (BSF)

  The PSF (or BSF) is a special case of the TAR when dose in air is compared to dose at the depth (d max ) of maximum dose  At this point the dose is maximum (peak) since the contribution of scatter is not offset by attenuation The term BSF applies strictly to situations where the depth of d max occurs at the surface of the phantom or patient (i.e. kV x rays)

The PSF versus Energy as a function of Field Size

  In general, scatter contribution decreases as energy increases Note:    Scatter can contribute as much as 50% to the dose a d max in kV beams The effect at percent (PSF 60 60 Co is of the order of a few Co 10x10 = 1.035

Increase in dose is greatest in smaller fields (note 5x5, 10x10, and 20x20)

TAR Dependencies

    Varies with energy like the pdd increases with energy.

Varies with field size like pdd- increases with field size.

Varies with depth like pdd- decreases with dept.

Assumed to be independent of SSD

The TPR and TMR

  Similar to the TAR, the TPR is the ratio of doses (D d and D t0 ) at two the source    Field sizes are equal Again field size is defined at depth of calculation Only attenuation by depth differs The TMR is a special case of the TPR when t equals the depth of d 0 max

TPR



D d

/

D t

0

TPR/TMR Dependencies

    Independent of SSD TMR increases with Energy TMR increases with field size TMR decreases with depth

Relationship between fundamental depth dependent quantities From: ICRU 14

PDD / TAR / BSF Relation

Approximate Relationships: PDD / TAR / BSF / TMR

BJR Supplement 17

Limitations of the application of inverse-square corrections

  It is generally believed that the TAR and TMR are independent of SSD This is true within limits  Note the effect of purely geometric distance corrections on the contribution of scatter

Effect of scatter vs. distance: TMR vs. field size

  The TMR (or TAR or PDD) for a given depth can be plotted as a function of field size  Shown here are TMRs at 1.5, 5.0, 10.0, 15.0, 20.0, 25.0, and 30.0 cm depths as a function of field size Note the lesser increase in TMR as a function of field size  This implies that differences in scatter are of greater significance in smaller fields than larger fields, and at closer distances to calculation points than farther distances Varian 2107 6 MV X Rays (K&S Diamond)

Scatter Factors

 Scatter factors describe field-size dependence of dose at a point    Need to define “field size” clearly  Many details … Often wise to separate sources of scatter   Scatter from the head of the treatment unit Scatter from the phantom or patient Measurements complicated by need for electronic equilibrium  Kerma to dose, again

Wedge Transmission

  Beam intensity is also affected by the introduction of beam attenuators that may be used modify the beam’s shape or intensity  Such attenuators may be plastic trays used to support field-shaping blocks, or physical wedges used to modify the beam’s intensity The transmission of radiation through attenuators is often field size and depth dependent

  Wedged dose distributions can be produced without physical attenuators   With “dynamic wedges”, a wedged dose distribution is produced by sweeping a collimator jaw across the field duration irradiation  The position of the jaw as a function of beam irradiation (monitor-unit setting) is given the wedge’s “segmented treatment table (STT)  The STT relates jaw position to fraction of total monitor unit setting The determination of dynamic wedge factors is relatively complex Gibbons

Off-Axis Quantities

  To a large degree, quantities and concepts discussed up to this point have addressed dose along the “central axis” of the beam It is necessary to characterize beam intensity “off-axis”   Two equivalent quantities are used  Off-Axis Factors (OAF)  Off-Center Ratios (OCR) These two quantities are equivalent

OAF

(

x

,

d

) 

D d

,

x

/

D d

, 0 where x = distance off-axis

Off-Axis Factors: Measured Profiles

 Off-axis factors are extracted from measured profiles  Profiles are smoothed, may be “symmetrized”, and are normalized to the central axis intensity

Off-Axis Factors: Typical Representations

 OAFs (OCRs) are often tabulated and plotted versus depth as a function of distance off axis   Where “distance off axis” means radial distance away from the central axis Note that, due to beam divergence, this distance varies with distance from the source 1.05

1.04

1.03

1.02

1.01

1.00

0.99

0.98

0.97

0.96

0.95

0.00

Varian 2100C SN 241 6 MV Open-Field Off-Axis Factors

0.10

0.02

0.04

0.06

Off-Axis "Tangent"

0.08

Depth 1.7

Depth 5.0

Depth 10 Depth 15 Depth 20 Depth 25 Depth 30

Off-Axis Wedge Corrections

 Descriptions vary of off-axis intensity in wedged fields   Measured profiles contain both open-field off-axis intensity as well as differential wedge transmission We have defined off-axis wedge corrections as corrections to the central axis wedge factor  Open-field off-axis intensity is divided out of the profile  The corrected profile is normalized to the central axis value

Examples

    The depth dose for a 6 MV beam at 10 cm depth for a 10 x 10 field; 100 cm ssd is 0.668. What is the percent depth dose if the ssd is 120 cm.

F=((120 +1.5)/(100+1.5)) 2 x((100 +10)/(120 +10)) 2 F= 1.026

dd at 120 ssd = 1.026 x 0.668 = 0.685

Example Problems

 What is the given dose if the dose prescribed is 200 cGy to a depth of 10 cm. 6X, 10 x 10 field, 100 cm SSD.

  DD at 10 cm for 10 x 10 is 0.668.

Given Dose is 200/0.668 = 299.4 cGy

Examples

     A single anterior 6MV beam is used to deliver 200 cGy to a depth of 5cm. What is the dose to the cord if it lies 12 cm from the anterior surface. Patient is set-up 100 ssd with a 10 x 15 field.

Equivalent square for 10 x 15 = 12cm 2 dd for 12 x 12 field at 5cm =.866

dd for 12 x 12 field at 12 cm = .608

Dose to cord = 200/.866 x .608 = 140.4 cGy

Examples      A patient is treated with parallel opposed fields to midplane. The patient is treated with 6 MV and has a lateral neck thickness of 12cm. The field size used is 6 x 6. The prescription is 200 cGy to midplane. What is the dose per fraction to a node located 3 cm from the right side. The patient is set-up 100 cm SSD.

dd at 6cm=0.810; dd at 9cm=.686 ; dd at 3 cm= 0.945

Dose to node from right= (100/.810) x 0.945 =116.7 cGy Dose to node from left = (100/.810) x .686 = 84.7 cGy Total dose = 116.7 + 84.7 = 201.4 cGy

Examples      A patient is treated with a single anterior field. Field Size is 8 x 14. Patient is set-up 100 cm SAD. Prescription is 200 cGy to a depth of 6cm. A 6 MV beam is used for treatment. What is the dose to a node that is 3 cm deep? Assume field size is at isocenter.

Equivalent square of field is 10.2 cm 2 TMR at 6cm = .8955

TMR at 3 cm = .9761

Dose to node = (200/.8955) x .9761 x (100/97) 2 = 231.7 cGy

Examples  A patient is treated with parallel opposed 6 MV fields. The patient’s separation is 20 cm. Prescription is to deliver 300 cGy to Midplane. Field size is 15 x 20.(100cm SAD) What is the dose to the cord on central axis if the cord lies 6cm from the posterior surface?

    Equivalent square is 17.1

TMR at 10 cm = .8063

TMR at 6 cm = .9088

TMR at 14 cm = .7041

Examples

      Dose to the Cord from the Anterior (150/.8063) x (100/104) 2 x .7041 = 121 cGy Dose to the Cord from the Posterior (150/.8063) x (100/96) 2 x .9088 = 183 cGy Total dose to the cord 183 +121 = 304 cGy